arXiv subjects

Andreas Schäfer

Publications and source records attributed to Andreas Schäfer.

At least 55 records · Page 3Linked to original sources

arXiv2023

Precision test of gauge/gravity duality in D0-brane matrix model at low temperature

We test the gauge/gravity duality between the matrix model and type IIA string theory at low temperatures with unprecedented accuracy. To this end, we perform lattice Monte Carlo simulations of the Berenstein-Maldacena-Nastase (BMN) matrix model, which is the one-parameter deformation of the Banks-Fischler-Shenker-Susskind (BFSS) matrix model, taking both the large $N$ and continuum limits. We leverage the fact that sufficiently small flux parameters in the BMN matrix model have a negligible impact on the energy of the system while stabilizing the flat directions so that simulations at smaller $N$ than in the BFSS matrix model are possible. Hence, we can perform a precision measurement of the large $N$ continuum energy at the lowest temperatures to date. The energy is in perfect agreement with supergravity predictions including estimations of $α'$-corrections from previous simulations. At the lowest temperature where we can simulate efficiently ($T=0.25λ^{1/3}$, where $λ$ is the 't Hooft coupling), the difference in energy to the pure supergravity prediction is less than $10\%$. Furthermore, we can extract the coefficient of the $1/N^4$ corrections at a fixed temperature with good accuracy, which was previously unknown.

hep-th↗

arXiv2023

Nucleon Transversity Distribution in the Continuum and Physical Mass Limit from Lattice QCD

We report a state-of-the-art lattice QCD calculation of the isovector quark transversity distribution of the proton in the continuum and physical mass limit using large-momentum effective theory. The calculation is done at four lattice spacings $a=\{0.098,0.085,0.064,0.049\}$~fm and various pion masses ranging between $220$ and $350$ MeV, with proton momenta up to $2.8$ GeV. The result is non-perturbatively renormalized in the hybrid scheme with self renormalization which treats the infrared physics at large correlation distance properly, and extrapolated to the continuum, physical mass and infinite momentum limit. We also compare with recent global analyses for the nucleon isovector quark transversity distribution.

hep-lat↗

arXiv2022

50 Years of Quantum Chromodynamics

This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed.

hep-ph↗

arXiv2022

Quark-Hadron Transition and Entanglement

The dual holographic description has enjoyed many successes in explaining fundamental properties of the early stages of relativistic heavy ion collisions up to the formation of a minimal-viscosity quark-gluon fluid. However, there have been few attempts to extend its application beyond this stage. Here we explore the prospects for such an extension beyond the time of hadronization. Our discussion makes use of recent insights into the duality of entanglement properties of field theory states in the edge of Anti-de Sitter space and non-trivial topologies of horizons in the bulk, often referred to as ER = EPR duality. We discuss this topic from the point of view of heavy-ion phenomenology, review several relevant concepts, and map out a path toward combining them into a comprehensive, at least semiquantitative description of relativistic heavy ion collisions. We outline possible next steps in this direction.

hep-ph↗

arXiv2022

Nonperturbative test of the Maldacena-Milekhin conjecture for the BMN matrix model

We test a conjecture by Maldacena and Milekhin for the ungauged version of the Berenstein-Maldacena-Nastase (BMN) matrix model by lattice Monte Carlo simulation. The numerical results reproduce the perturbative and gravity results in the limit of large and small flux parameter, respectively, and are consistent with the conjecture.

hep-th↗

arXiv2022

Confinement/deconfinement transition in the D0-brane matrix model -- A signature of M-theory?

We study the confinement/deconfinement transition in the D0-brane matrix model (often called the BFSS matrix model) and its one-parameter deformation (the BMN matrix model) numerically by lattice Monte Carlo simulations. Our results confirm general expectations from the dual string/M-theory picture for strong coupling. In particular, we observe the confined phase in the BFSS matrix model, which is a nontrivial consequence of the M-theory picture. We suggest that these models provide us with an ideal framework to study the Schwarzschild black hole, M-theory, and furthermore, the parameter region of the phase transition between type IIA superstring theory and M-theory. A detailed study of M-theory via lattice Monte Carlo simulations of the D0-brane matrix model might be doable with much smaller computational resources than previously expected.

hep-th↗

arXiv2022

T-odd proton-helicity asymmetry in semi-inclusive DIS in perturbative QCD

We compute the single-spin asymmetry $A_{UL}$ in semi-inclusive deep-inelastic scattering of unpolarized leptons and longitudinally polarized protons at large transverse momentum of the produced hadron. Our calculation is performed in collinear factorization at the lowest order of QCD perturbation theory. For photon exchange the asymmetry is T-odd and receives contributions from the interference of the tree level and one-loop absorptive amplitudes. We consider the behavior of the spin asymmetry at low transverse momentum where contact to the formalism based on transverse-momentum dependent distribution functions can be made. We also present some phenomenological results relevant for the COMPASS and HERMES experiments and the future Electron-Ion Collider.

hep-ph↗

arXiv2022

Nonperturbative Determination of Collins-Soper Kernel from Quasi Transverse-Momentum Dependent Wave Functions

In the framework of large-momentum effective theory at one-loop matching accuracy, we perform a lattice calculation of the Collins-Soper kernel which governs the rapidity evolution of transverse-momentum-dependent (TMD) distributions. We first obtain the quasi TMD wave functions at three different meson momenta on a lattice with valence clover quarks on a dynamical HISQ sea and lattice spacing $a=0.12$~fm from MILC, and renormalize the pertinent linear divergences using Wilson loops. Through one-loop matching to the light-cone wave functions, we determine the Collins-Soper kernel with transverse separation up to 0.6~fm. We study the systematic uncertainties from operator mixing and scale dependence, as well as the impact from higher power corrections. Our results potentially allow for a determination of the soft function and other transverse-momentum dependent quantities at one-loop accuracy.

hep-lat↗

arXiv2022

Mellin moments of spin dependent and independent PDFs of the pion and rho meson

We compute the second moments of pion and rho parton distribution functions (PDFs) in lattice QCD with $N_f = 2+1$ flavors of improved Wilson fermions. We determine both singlet and non-singlet flavor combinations and, for the first time, take disconnected contributions fully into account. In the case of the rho, we also calculate the additional contribution arising from the $b_1$ structure function. The numerical analysis includes 26 ensembles, mainly generated by the CLS effort, with pion masses ranging from 420MeV down to 214MeV and with 5 different lattice spacings in the range of 0.1fm to 0.05fm. This enables us to take the continuum limit, as well as to resolve the quark mass dependencies reliably. Additionally we discuss the contaminations of rho correlation functions by two-pion states.

hep-lat↗

arXiv2022

Pion and Kaon Distribution Amplitudes from Lattice QCD

We present the state-of-the-art lattice QCD calculation of the pion and kaon light-cone distribution amplitudes (DAs) using large-momentum effective theory. The calculation is done at three lattice spacings $a\approx\{0.06,0.09,0.12\}$ fm and physical pion and kaon masses, with the meson momenta $P_z = \{1.29,1.72,2.15\}$ GeV. The result is non-perturbatively renormalized in a recently proposed hybrid scheme with self renormalization, and extrapolated to the continuum as well as the infinite momentum limit. We find a significant deviation of the pion and kaon DAs from the asymptotic form, and a large $SU(3)$ flavor breaking effect in the kaon DA.

hep-lat↗

arXiv2022

BITES: Balanced Individual Treatment Effect for Survival data

Estimating the effects of interventions on patient outcome is one of the key aspects of personalized medicine. Their inference is often challenged by the fact that the training data comprises only the outcome for the administered treatment, and not for alternative treatments (the so-called counterfactual outcomes). Several methods were suggested for this scenario based on observational data, i.e.~data where the intervention was not applied randomly, for both continuous and binary outcome variables. However, patient outcome is often recorded in terms of time-to-event data, comprising right-censored event times if an event does not occur within the observation period. Albeit their enormous importance, time-to-event data is rarely used for treatment optimization. We suggest an approach named BITES (Balanced Individual Treatment Effect for Survival data), which combines a treatment-specific semi-parametric Cox loss with a treatment-balanced deep neural network; i.e.~we regularize differences between treated and non-treated patients using Integral Probability Metrics (IPM). We show in simulation studies that this approach outperforms the state of the art. Further, we demonstrate in an application to a cohort of breast cancer patients that hormone treatment can be optimized based on six routine parameters. We successfully validated this finding in an independent cohort. BITES is provided as an easy-to-use python implementation.

stat.ME↗

arXiv2021

Double parton distributions in the nucleon from lattice QCD

We evaluate nucleon four-point functions in the framework of lattice QCD in order to extract the first Mellin moment of double parton distributions (DPDs) in the unpolarized proton. In this first study, we employ an nf = 2 + 1 ensemble with pseudoscalar masses of mpi = 355 MeV and mK = 441 MeV. The results are converted to the scale mu = 2 GeV. Our calculation includes all Wick contractions, and for almost all of them a good statistical signal is obtained. We analyze the dependence of the DPD Mellin moments on the quark flavor and the quark polarization. Furthermore, the validity of frequently used factorization assumptions is investigated.

hep-lat↗

arXiv2021

Masses and decay constants of the $η$ and $η^\prime$ mesons from lattice QCD

We determine the masses, the singlet and octet decay constants as well as the anomalous matrix elements of the $η$ and $η^\prime$ mesons in $N_f=2+1$ QCD\@. The results are obtained using twenty-one CLS ensembles of non-perturbatively improved Wilson fermions that span four lattice spacings ranging from $a\approx 0.086\,$fm down to $a\approx 0.050\,$fm. The pion masses vary from $M_π=420\,$MeV to $126\,$MeV and the spatial lattice extents $L_s$ are such that $L_sM_π\gtrsim 4$, avoiding significant finite volume effects. The quark mass dependence of the data is tightly constrained by employing two trajectories in the quark mass plane, enabling a thorough investigation of U($3$) large-$N_c$ chiral perturbation theory (ChPT). The continuum limit extrapolated data turn out to be reasonably well described by the next-to-leading order ChPT parametrization and the respective low energy constants are determined. The data are shown to be consistent with the singlet axial Ward identity and, for the first time, also the matrix elements with the topological charge density are computed. We also derive the corresponding next-to-leading order large-$N_{c}$ ChPT formulae. We find $F^8 = 115.0(2.8)~\text{MeV}$, $θ_{8} = -25.8(2.3)^{\circ}$, $θ_0 = -8.1(1.8)^{\circ}$ and, in the $\overline{\mathrm{MS}}$ scheme for $N_f=3$, $F^{0}(μ= 2\,\mathrm{GeV}) = 100.1(3.0)~\text{MeV}$, where the decay constants read $F^8_η=F^8\cos θ_8$, $F^8_{η^\prime}=F^8\sin θ_8$, $F^0_η=-F^0\sin θ_0$ and $F^0_{η^\prime}=F^0\cos θ_0$. For the gluonic matrix elements, we obtain $a_η(μ= 2\,\mathrm{GeV}) = 0.0170(10)\,\mathrm{GeV}^{3}$ and $a_{η^{\prime}}(μ= 2\,\mathrm{GeV}) = 0.0381(84)\,\mathrm{GeV}^{3}$, where statistical and all systematic errors are added in quadrature.

hep-lat↗

arXiv2021

Determination of the Collins-Soper Kernel from Lattice QCD

We present lattice results for the non-perturbative Collins-Soper (CS) kernel, which describes the energy-dependence of transverse momentum-dependent parton distributions (TMDs). The CS kernel is extracted from the ratios of first Mellin moments of quasi-TMDs evaluated at different nucleon momenta.The analysis is done with dynamical $N_f=2+1$ clover fermions for the CLS ensemble H101 ($a=0.0854\,\mathrm{fm}$, $m_π=m_K=422\,\mathrm{MeV}$). The computed CS kernel is in good agreement with experimental extractions and previous lattice studies.

hep-lat↗

arXiv2021

RI/MOM renormalization of the quasi-PDF in lattice regularization

We analyze the lattice spacing dependence for the pion unpolarized matrix element of a quark bilinear operator with Wilson link (quasi-PDF operator) in the rest frame, using 13 lattice spacings ranging from 0.032 fm to 0.121 fm. We compare results for three different fermion actions with or without good chiral symmetry on dynamical gauge ensembles from three collaborations. This investigation is motivated by the fact that the gauge link generates an $1/a$ divergence, the cancelation of which in many ratios can be numerically tricky. Indeed, our results show that this cancelation deteriorates with decreasing lattice spacing, and that the RI/MOM method leaves a linearly divergent residue for quasi-PDFs. We also show that in the Landau gauge the interaction between the Wilson link and the external state results in a linear divergence which depends on the discretized fermion action.

hep-lat↗

arXiv2021

Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum

In classical chaotic systems the entropy, averaged over initial phase space distributions, follows an universal behavior. While approaching thermal equilibrium it passes through a stage where it grows linearly, while the growth rate, the Kolmogorov-Sinai entropy, is given by the sum over all positive Lyapunov exponents. A natural question is whether a similar relation is valid for quantum systems. We argue that the Maldacena-Shenker-Stanford bound on quantum Lyapunov exponents $λ$ implies that the upper bound on the growth rate of the entropy, averaged over states in Hilbert space that evolve towards a thermal state with temperature $T$ and entropy $S_{eq}$, should be given by $S_{eq} πT =\sum_{λ>0}2 πT$. Strongly coupled, large $N$ theories with black hole duals should saturate the bound. By studying a large number of isotropization processes of random, spatially homogeneous, far from equilibrium initial states in large $N$, $\mathcal{N}=4$ Super Yang Mills theory at strong coupling and computing the ensemble averaged growth rate of the dual black hole's apparent horizon area, we find both an analogous behavior as in classical chaotic systems and numerical evidence that the conjectured bound on averaged entropy growth is saturated granted that the Lyapunov exponents are degenerate $λ= \pm 2 πT$. This fits to the behavior of classical systems with plus/minus symmetric Lyapunov spectra, a symmetry which implies the validity of Liouville's theorem.

hep-th↗

arXiv2021

Scale symmetry breaking, quantum anomalous energy and proton mass decomposition

We study the anomalous scale symmetry breaking effects on the proton mass in QCD due to quantum fluctuations at ultraviolet scales. We confirm that a novel contribution naturally arises as a part of the proton mass, which we call the quantum anomalous energy (QAE). We discuss the QAE origins in both lattice and dimensional regularizations and demonstrate its role as a scheme-and-scale independent component in the mass decomposition. We further argue that QAE role in the proton mass resembles a dynamical Higgs mechanism, in which the anomalous scale symmetry breaking field generates mass scales through its vacuum condensate, as well as its static and dynamical responses to the valence quarks. We demonstrate some of our points in two simpler but closely related quantum field theories, namely the 1+1 dimensional non-linear sigma model in which QAE is non-perturbative and scheme-independent, and QED where the anomalous energy effect is perturbative calculable.

hep-ph↗

arXiv2021

Self-Renormalization of Quasi-Light-Front Correlators on the Lattice

In applying large-momentum effective theory, renormalization of the Euclidean correlators in lattice regularization is a challenge due to linear divergences in the self-energy of Wilson lines. Based on lattice QCD matrix elements of the quasi-PDF operator at lattice spacing $a$= 0.03 fm $\sim$ 0.12 fm with clover and overlap valence quarks on staggered and domain-wall sea, we design a strategy to disentangle the divergent renormalization factors from finite physics matrix elements, which can be matched to a continuum scheme at short distance such as dimensional regularization and minimal subtraction. Our results indicate that the renormalization factors are universal in the hadron state matrix elements. Moreover, the physical matrix elements appear independent of the valence fermion formulations. These conclusions remain valid even with HYP smearing which reduces the statistical errors albeit reducing control of the renormalization procedure. Moreover, we find a large non-perturbative effect in the popular RI/MOM and ratio renormalization scheme, suggesting favor of the hybrid renormalization procedure proposed recently.

hep-lat↗